The radius of a circle is the distance from the center of the circle to any point on the circle. It is denoted by the letter "r". The radius is a fundamental measurement in the study of circles and is used in various calculations related to circles, such as finding the circumference, area, and diameter.

To calculate the radius of a circle, you can use the formula:

**r = c / (2π)**

Where "c" is the circumference of the circle and "π" is a mathematical constant approximately equal to 3.14159.

Some key properties of the radius include:

- The radius is always half the length of the diameter of the circle.
- All radii of the same circle are congruent (they have the same length).
- The radius is perpendicular to any tangent line drawn to the circle at the point of contact.

When studying the concept of radius, it's important to understand the following:

- Definition of the radius and its significance in the context of a circle.
- How to calculate the radius using the formula
**r = c / (2π)**. - Relationship between the radius and diameter of a circle.
- Practical applications of the radius in real-life situations, such as measuring the size of circular objects.
- Solving problems involving the radius, circumference, and area of circles.

Understanding the concept of radius is crucial for further studies in geometry, trigonometry, and other branches of mathematics that deal with circular shapes and measurements.

.Study GuideMeasurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.